Let the Study Guides explain the CAST diagram and how to solve Trig Equations. See below ...

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Resources used with students studying Maths in Scottish Secondary Schools

Understanding Trig Equations is important to ensure your success in tests, assessments and exams.

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________________ | ____________________________ |

Exam Ques 1 (N5) | Trig Equations |

Exam Ques 1 (N5) | Trig Graphs & Equations |

Exam Ques 3 (N5) | Further Trig |

Mind Map 1 | Solving Trig Equations |

Mind Map 2 | Solving Trig Equations (PowerPoint) |

PowerPoint | Trig Graphs |

Video | Trig (Right Angled Triangles) |

A Trig Equations exam question where you are asked *“to solve the equation for 0 ≤ x ≤ 360°” *is shown below*:*

* 11cosx° – 2 = 3*

Source: N5 Maths, 2014, P2, Q12

Solving equations such as *sin x° = 1, sin x° = – 1* and *cos x° = 0* can be achieved just be reading the solutions from the trig graphs.

For example, in the graph of* y = sin x°* below, it can be seen that if we draw a horizontal line from 1 on the y-axis then it will meet the sin wave at 90°. Therefore the solution to* sin x° = 1* is *x = 90°.*

Solving Trig Equations such as *sin x° = 0.5* is more complicated**. **

In the graph of* y = sin x°* above, it can be seen that if we draw a horizontal line from 0.5 on the y-axis then it will meet the sin wave at two places.

A calculator is required for the first solution:

* x = inverse sin (0.5) = 30°*

and the correct use of the CAST diagram is required to find the second solution:

* x = 180° – 30° = 150°*

We cover everything you need to know about the Trig Equations in the Study Guides.

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